Plant identification in a stochastic closed-loop system

A plant is to be identified in a closed system subjected to unobservable noises correlated in time. A class of closed systems with interrelated noises acting on the plant and the controller is studied. The plant is shown to be identifiable in a closed system without simultaneous identification of the controller. To study this problem the notion of a truncated likelihood function is introduced. Sufficient conditions are obtained for convergence almost certainly of estimates for truncated likelihood of plant parameters to true values with noise acting on the plant in the absence of noise in the control channel is studied. The concept of structural non-identif lability of a system is introduced. Conditions of structural non-identifiability are obtained for a class of closed systems without noise in the control channel.